2. The amount of heat required to raise the temperature of one gram of the solid is called the heat capacity. The temperature of solid continuously increases until it reaches to its
melting point. At melting point the temperature will hold steady for a while, even though heat is added to the solid. It will hold steady until the solid completely melts. The
temperature rising stops because melting requires energy. All the energy added to a crystalline solid at its melting point goes into melting, and none of it goes into raising the
temperature. Then again, the temperature of the solid will begin to increase. This heat is called the latent heat of melting. Once the solid get melted, the temperature begins to
rise but at a slower rate. The molten solid (liquid) has a higher heat capacity than the solid crystalline state therefore it absorbs more heat with a smaller increase in
temperature.
Hence, when a crystalline solid melt it absorbs a certain amount of heat, the latent heat of melting, and it undergoes a change in its heat capacity. Any change like melting,
freezing, boiling or condensation brought about by heat which has a change in heat capacity and a latent heat involved, is called a first order transition. But when an
amorphous solid is heated to its Tg, the temperature increases. It increases at a rate determined by the solid’s heat capacity. There is no latent heat of glass transition. At Tg,
the temperature does not stop rising. The temperature keeps upon increasing above Tg but at different rate than below Tg. The solid does undergo an increase in its heat
capacity when it undergoes the glass transition due to change in heat capacity. Any change brought about by heat, which has a change in heat capacity, but a latent heat is not
involved, is called a second order transition. In first order transition melting is observed with crystalline solid, and in second order transition the glass transition is observed with
amorphous solid.
3. Physical properties of liquids are controlled by strength and nature of intermolecular attractive forces. The most
important properties are vapour pressure, viscosity, surface tension and light absorption and refraction. A liquid
placed in a container partially evaporates to establish a pressure of vapour above the liquid. The established
pressure depends on the nature of the liquid, and at equilibrium it becomes constant at any given temperature.
This constant vapour pressure is the saturated vapour pressure of liquid at that temperature. Until the vapour
pressure is maintained, no further evaporation observes. As shown in Fig. 2.6, at lower pressures a liquid
evaporates into the vapour phase while at higher pressure the vapour tend to condensate till equilibrium
establishes. During vaporization heat is absorbed by liquid. At any given temperature, the amount of heat
required per gram of liquid is definite quantity called as heat of vaporization of liquid (∆Hv). It is difference in
enthalpies of vapour (Hv) and liquid (Hl), respectively. Therefore, ∆Hv = Hv – Hl … (2.1) During evaporation ∆Hv is
always positive while during condensation it becomes always negative. As per definition of change of enthalpy,
∆Hv is the difference in internal energy of vapour and liquid. ∆Hv = ∆Ev + P ∆Vv … (2.2) where, P is vapour
pressure and ∆Hv is change in volume during vapour to liquid transition. Partial vapour pressure Condensation
Evaporation Water
4. Figure 2.6: Schematic Showing Evaporation and Condensation in Liquids with Change in
Temperature
The temperature of a substance depends on the average kinetic energy of its molecules. Average kinetic
energy is considered because there is an enormous range of kinetic energies for these molecules. Even
at temperatures well below the boiling point of a liquid, some of the particles are moving fast enough to
escape from the liquid. During this process the average kinetic energy of the liquid decreases. As a
result, the liquid becomes cooler. It therefore absorbs energy from its surroundings until it returns to
thermal equilibrium. But as soon as this happens, some of the water molecules once again have enough
energy to escape from the liquid.
Figure 2.7: Closed Container Showing Vapour Pressure of Liquid at Given Temperature
5. In an open container, this process continues until all the water evaporates. In a closed container, some of the molecules
escape from the surface of the liquid to form a vapour. Eventually, the rate at which the liquid evaporates to form a gas
becomes equal to the rate at which the vapour condenses to form the liquid. At this point, the system is said to be in
equilibrium. As shown in Fig. 2.7, the space above the liquid is saturated with water vapour, and no more water
evaporates. The pressure of the water vapour in a closed container at equilibrium is called the vapour pressure.
Figure 2.8: Plot of Vapour Pressure versus Temperature of Water
The Fig. 2.8 shows that the relationship between vapour pressure and temperature is not linear. The vapour pressure of water
increases more rapidly than the temperature of the system.
Measurement of Vapour Pressure: Vapour pressures of liquids are measured by static and dynamic methods.
Static Method: Vapour pressure of liquid is generally measured by the isoteniscopic method, which is precise, flexible and
convenient over a range of temperatures. A simple apparatus is shown in Fig. 2.9. It consist essentially an isoteniscopic bulb of
2 cm diameter.
6. Figure 2.9: Schematic of Isoteniscopic Method
A liquid under test is filled in bulb-up to half level mark, which is connected to mercury manometer and a pump. The air
inside the bulb is removed by application of vacuum. Now there is no air present in the bulb. To maintain equilibrium, part of
liquid evaporates. The system is maintained at constant temperature so that the equilibrium between liquid and vapour
attains. The generated vapours exert pressure on mercury present in column. The difference in height of mercury in column
is determined which is equal to vapour pressure of that liquid. By maintaining the system at any other temperature, it is
possible to determine vapour pressure at that temperature. This method is used for liquids having vapour pressures on
higher sides close to one atmosphere.
Dynamic Method:
This method is proposed by Walker and is useful especially in determinations of very low vapour pressure of liquid mixtures.
Great care is required to obtain excellent results. An illustrative apparatus is shown in Fig. 2.10. An inert gas such as
nitrogen is passed through the given liquid at constant temperature. The inert gas is saturated with the vapours of liquid
under test and leaves the flask at exit of the tube. If P is total vapour pressure in the apparatus at saturation, n is the moles
of gas passed through and nv is number of moles of vapour collected. The nv is given as nv = Wv Mv
7. where, Wv is loss in weight of liquid and Mv is molecular weight of liquid. The partial
pressure of vapour, P’ is same as vapour pressure of liquid at saturation and can be given as
P’ =
𝑛
𝑛+1
Figure 2.10: Schematic of Dynamic Walker‘s Method
In the other form equation (2.4) can be written as P = m /MV × RT
where, m is loss in weight of liquid as vapour, V is volume of gas passed through, M is molecular
weight of liquid and R is gas constant.
8. Sublimation is another form of phase transitions. Here solid turns directly into a gas. As a sublimating material
changes from a solid to a gas, it never passes through the liquid state. As we know water exists in its three
forms namely ice, water, and steam. Sublimation is just one of the ways water or another substance can
change between its potential phases. Substances such as water and carbon dioxide (CO2) can be plotted on
as pressure vs. temperature to understand their state of matter (solid, liquid, or gas) at a given temperature
and pressure. At a typical atmospheric pressure, water is a solid at temperatures below 0° C, a liquid from 0 to
100° C, and a gas at higher temperatures. But atmospheric pressure, however, can change, particularly with
altitude. Higher altitudes yield lower atmospheric pressures. Water doesn't always change phase at the same
temperatures. For example, with lower pressures, liquid water changes to a gas at temperatures lower than
100° C. If the pressure is dropped low enough, water reaches what's known as a triple point. At pressure and
temperature of triple point a substance can exist in solid, liquid, and gaseous forms.
Below this point, solid water sublimes, changing directly into a gas with a rise in temperature and never pass
through the liquid phase. The CO2 has a triple point at a pressure higher than 1 atmospheric pressure,
meaning that at Earth's standard atmospheric pressure, CO2 will sublime as it heats and is converted from
solid to a gas.
9. A liquid need not always have to be heated to its boiling point before it changes to a gas. The kinetic energy
of the molecules is proportional to the absolute temperature of the gas. Due to high kinetic energy gas
molecules are in the state of constant motion. In liquids, only few molecules have lower or higher kinetic
energy.
It is illustrated in Fig. 2.11. At low temperature, the number of molecules having high kinetic energy is less
as shown by ABCD while at high temperature the number of molecules having higher kinetic energy
increases as shown by FBCE. The molecules with high kinetic energy are important to escape from liquid
state to vapour state. Upon cooling, kinetic energy gradually decreases. Since the temperature being
decreased a stage is attained at which gas molecules loses their energy that they are unable to overcome
forces of attraction between them. This situation brings the gas molecules near to have contact with each
other achieving more condensed liquid state. This state also can be possible to achieve by increasing
pressure of the gas but it has a limitation that pressure is effective only below specific temperature. This
temperature is called as critical temperature. It is defined as the temperature above which gas cannot be
liquefied, even if very high pressure is applied.
10. Figure 2.11: Energy Distribution of Molecules in Liquid
The critical temperature of water is 374 °C or 647 K and its critical pressure is 218 atm. If liquid
such as water is sealed in evacuated tube, a specific amount of it evaporates to produce vapour
at constant temperature. Like gas, water vapour exerts pressure and maintains equilibrium
between liquid and vapour phases. Exerted vapour pressure is characteristic of every liquid and
is constant at any given temperature. The vapour pressure of water at 25 °C is 23.76 mmHg
while at 10 °C it is 760 mmHg and therefore it is clear that vapour pressure increases
continuously with temperature. As water is heated further, it evaporates to more amount
resulting in increased vapour pressure.
11. When temperature reaches 374 °C the water meniscus becomes invisible. At critical temperature,
physical properties of liquid and vapour become identical and no distinction can be made between the
two. This point is also called as critical point. The temperature, saturated vapour pressure and molar
volume corresponding to this point are designated as critical temperature (Tc), critical pressure (Pc) and
critical volume (Vc) respectively. For water these critical constants are; Tc = 374 K, Pc = 219.5 atm and
Vc = 58.7 mL/mole. The critical points for different gases are given in Table 2.4.
Table 2.4: Critical Temperatures, Pressures and Boiling Points of Common Gases
